Problem: What do the following two equations represent? $4x-2y = -5$ $10x+20y = -3$
Solution: Putting the first equation in $y = mx + b$ form gives: $4x-2y = -5$ $-2y = -4x-5$ $y = 2x + \dfrac{5}{2}$ Putting the second equation in $y = mx + b$ form gives: $10x+20y = -3$ $20y = -10x-3$ $y = -\dfrac{1}{2}x - \dfrac{3}{20}$ The slopes are negative inverses of each other, so the lines are perpendicular.